Normally, opening one of the pause menu or the console will lock you out of the other. However, if the keys are pressed simultaneously, both can be opened at once, with the UI partially obscuring the console. This can lead to further odd behavior, such as the following:

Type while in this state -> Keypresses are sent to the console while the pause menu is open. Going into save, load, or controls sub-menu will prevent further keypresses from being sent to the console. Pressing console key does not close the console.

Press escape from this state -> player can move freely while console is on screen. Keypresses are still sent to the console, unless save, load, or controls sub-menu was accessed. Pressing console key closes the console.

Load a save from this state -> console remains on the screen and player can move freely. Keypresses aren't sent to the console. Pressing console key closes the console.

(The input window for the simultaneous pause+console keypresses is kind of tight.)